Molecular mechanisms of cellular mechanicsw

Mu Gao,ab

Marcos Sotomayor,ab

Elizabeth Villa,ac

Eric H. Leeacd

and

Klaus Schulten*abc

Received 27th April 2006, Accepted 19th June 2006

First published as an Advance Article on the web 10th July 2006

DOI: 10.1039/b606019f

Mechanical forces play an essential role in cellular processes as input, output, and signals.

Various protein complexes in the cell are designed to handle, transform and use such forces. For

instance, proteins of muscle and the extracellular matrix can withstand considerable stretching

forces, hearing-related and mechanosensory proteins can transform weak mechanical stimuli into

electrical signals, and regulatory proteins are suited to forcing DNA into loops to control gene

expression. Here we review the structure–function relationship of four protein complexes with

well defined and representative mechanical functions. The first example is titin, a protein that

confers passive elasticity on muscle. The second system is the elastic extracellular matrix protein,

fibronectin, and its cellular receptor integrin. The third protein system is the transduction

apparatus in hearing and other mechanical senses, likely containing cadherin and ankyrin repeats.

The last system is the lac repressor protein, which regulates gene expression by looping DNA.

This review focuses on atomic level descriptions of the physical mechanisms underlying the

various mechanical functions of the stated proteins.

Introduction

Biological cells utilize molecular compounds as well as me-

chanical forces as input, output, and signals. While the

transformation of chemical compounds by cells, e.g., through

enzymes, has been studied for decades, much less is known

about the transformation of mechanical forces. Just as cells

transform chemical compounds, they also transform mechan-

ical forces. Examples are motor proteins with forces as

output,1 F1 ATP synthase with torque as input,2,3 or mechan-

osensitive channels with force as a signal.4 The mechanical

forces that arise in cells amount to a few pN in single proteins,

but can be much larger in multi-protein filaments that experi-

ence cellular scale strain.

Obviously, the cell needs proteins that can sustain mechan-

ical forces. Examples are the forces arising in sarcomeric

muscle cells where the cell uses the protein titin5,6 to maintain

structural integrity and provide passive elasticity for the

muscle sarcomere.

In order to detect mechanical forces as signals, cells need to

respond to such forces through significant, yet reversible

structural changes. Examples are the proteins, not yet un-

ambiguously identified, that form the transduction apparatus

in inner ear hair cells capable of detecting the weak acoustical

forces arising in the cochlea.7,8 Other examples are the trans-

membrane proteins involved in transduction of force signals

across cellular membranes9 and the extracellular matrix pro-

teins designed to connect cells in tissues.10

Forces also arise within cells in numerous other circum-

stances where one might not expect them off-hand. An exam-

ple is the regulation of the genome where, due to the

macroscopic length of the cellular DNA, strong coiling forces

arise that regulatory proteins need to sustain.11 In fact, many

regulatory proteins deform the DNA through formation of

kinks and loops.12

What is the physical mechanism underlying the mechanical

functions of proteins? To address this question one may follow

the conventional route of inspecting equilibrium protein struc-

tures. However, in the present case such structures are of only

limited value since they typically do not reflect the mechanical

properties connected with significant structural deformation

induced by forces. Fortunately, there exist today numerous

experimental methodologies for directly probing mechanical

responses of a single biopolymer. Key methods are atomic

force microscopy (AFM),13,14 laser optical tweezers,15,16 fluor-

escence resonance energy transfer,17–19 and biomembrane

force probe.20 It was due to these novel methods that the

study of active and passive mechanical systems in cells experi-

enced a rapid development; yet, all these methods reveal only

very limited microscopic detail on biopolymer mechanics, e.g.,

in the case of AFM experiments observables are only a rupture

force value and the associated extension.21 This is where

molecular dynamics modeling can contribute significantly.

Molecular dynamics has the ability to probe the passive

mechanical properties of proteins by application of external

forces. The methodology, best known as steered molecular

dynamics (SMD), has been developed over the last decade and

achieved notable successes in relating structure, function, and

a Beckman Institute, University of Illinois at Urbana-Champaign,Urbana, IL, USA. E-mail: kschulte@ks.uiuc.edu

bDepartment of Physics, University of Illinois at Urbana-Champaign,Urbana, IL, USA

cCenter for Biophysics and Computational Biology, University ofIllinois at Urbana-Champaign, Urbana, IL, USA

dCollege of Medicine, University of Illinois at Urbana–Champaign,Urbana, IL, USA

w Presented at the 87th International Bunsen Discussion Meeting onMechanically Induced Chemistry - Theory and Experiment, Tutzing,Munich, Germany, October 3–6, 2005.

3692 | Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 This journal is �c the Owner Societies 2006

INVITED ARTICLE www.rsc.org/pccp | Physical Chemistry Chemical Physics

observation to physical mechanisms permitting biopolymers,

in particular proteins, to bear the forces arising from natural

cellular processes.22–45

It is certainly not possible to cover all aspects of cellular

mechanical processes in this short review. Instead, we choose

four protein systems where SMD studies have provided crucial

structural insights into the molecular mechanisms underlying

the functions of these proteins. We discuss the mechanical

properties of the protein titin that determines the passive

elasticity of muscle, the elastic extracellular matrix protein

fibronectin and its cellular receptor integrins, the proteins

ankyrin and cadherin likely involved in mechanotransduction

in the inner ear and other mechanical senses, and the lac

repressor protein that regulates gene expression by looping

DNA. We apologize to all researchers whose pioneering work

cannot be reviewed due to the space limit.

Steered molecular dynamics

SMD is an ideal computational tool to probe mechanical

properties of biopolymers at the atomic level. SMD can induce

conformational changes on time scales covered by molecular

dynamics simulations, i.e., typically a few tens of nanoseconds.

For this purpose, external forces are applied, e.g., between the

termini of a protein; the forces and the response of the

biopolymer, e.g., linear extension, are recorded and subse-

quently analyzed. The SMD approach, reviewed in ref. 26, 46,

47, has provided important insights into molecular mechan-

isms of cellular mechanics for ligand–receptor binding,22–25,48

cellular adhesion,27–29 force generation,49 transduction of

mechanical signals,50–52 regulation of gene expression,44,53

and protein elasticity.30–39,41–43,54–56

There are many ways forces can be applied in SMD

simulations. This is achieved through protocols defining typi-

cally how force strength and direction varies as a function of

time. In the simplest case one specifies a constant force;

another typical protocol corresponds to connecting a set of

atoms to a harmonic spring, the end of which is pulled with

constant velocity.26 Forces can also be applied interactively in

an ongoing simulation by means of a so-called haptic de-

vice.57,58 These and other force protocols have been imple-

mented in NAMD,59 the MD program employed in all the

SMD studies reviewed here. The constant velocity SMD

protocol mimics AFM experiments in which a molecule is

stretched by a cantilever moving at constant velocity. This

protocol easily induces conformational transitions since force

can rise to very large values; this advantage is outweighed by

the lack of explicit control of the force. The constant force

SMD protocol permits selection of the force magnitude such

that key conformational transitions, unresolved in constant

velocity protocols, are captured in ‘‘slow motion’’. Through

NAMD one can define linear forces as well as torque. In

addition to these built-in features, NAMD also provides a

scripting interface that allows one to customize SMD proce-

dures for complex force protocols,59 such as simulating the

membrane surface tension acting on a mechanosensitive chan-

nel51 or forces due to DNA looping acting on a regulatory

protein.44 The most flexible force protocol is available within

interactive molecular dynamics simulations, in which case

linear force or torque can be issued and varied by the user

on the fly in an ongoing simulation with visual and mechanical

feedback.57,58

A limitation of the modeling approach, however, is the short

time scale accessible to MD, several orders of magnitude

shorter than the time scale of AFM observations. As a result,

peak forces calculated in SMD simulations are typically one

order of magnitude higher than those obtained from AFM

experiments. Despite this difference, SMD simulations have

generated trajectories with features that are in close agreement

with AFM experiments, such as the extension of intermedi-

ates33,41 and the relative mechanical stability of a group of

proteins.42 For a protein with multiple unfolding pathways

under the same pulling geometry, SMD simulations can reveal

these pathways and suggest mutants discerning pathways

experimentally.40,54,60 Extended simulation times lead to im-

proved convergence with observation.32 Nevertheless, one

should abstain from focusing on peak forces when comparing

simulation and observation and instead focus on energetics

and related mean first passage times.32,61

The observables monitored in SMD simulations, typically

force and extension as a function of time, need to be analyzed

in terms of quantitative measures of protein mechanical

properties such as elastic moduli or potentials of mean force

(PMF) along a stretching direction. For this purpose analysis

methodologies have been developed based on non-equilibrium

statistical mechanics for the calculation of the PMF61 and on

mean first passage times.22,32,40

An extension-time profile obtained from a constant force

SMD simulation usually displays plateaus corresponding to

unfolding/unbinding barrier crossing processes. The length of

a plateau indicates the first passage time spent in crossing the

barrier. The applied force effectively lowers the barrier such

that stronger forces lead to faster barrier crossing than weaker

forces. In all cases, the stretching motion gets temporarily

‘‘stuck’’ in front of the barrier, which is then overcome by

thermal fluctuations. This scenario can be described as Brow-

nian motion governed by a potential which is the sum of the

indigenous barrier and a linear potential accounting for the

applied force. The mean time tbarrier to cross the barrier can be

evaluated using the expressions for the mean first passage

time.62–64 An analytical expression of tbarrier exists for a

linearly increasing ramp model for the PMF.22 By comparing

the mean first passage times with the respective times tbarrierfor various forces, one can estimate the height of the indigen-

ous potential barrier. Using this approach, the height of the

major unfolding barrier of titin I2732 and fibronectin mod-

ules37,42 have been estimated, the results being in close agree-

ment with AFM experiments.21,65

The mean first passage time method for sampling trajec-

tories from constant force pulling requires an estimate for the

PMF and provides limited information regarding the PMF,

mainly the height of the potential barrier associated with

unfolding/unbinding. Based on the Jarzynski equality,66–68 a

new method for sampling trajectories obtained from constant

velocity pulling has been proposed to reconstruct the PMF

without any assumption on its shape.69

The Jarzynski equality relates the free energy difference

DG= GB � GA, whereGA and GB correspond to the free energy

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at states A and B, to work W enforcing the transition A - B

through non-equilibrium processes. The equation reads

exp(�bDG) = hexp(�bW)i (1)

where b = 1/kBT is the inverse temperature and kB is the

Boltzmann constant. The Jarzynski equality provides a means

to extract DG from averaging, denoted by h� � �i, over A - B

non-equilibrium processes, such as SMD stretching. Unfortu-

nately, the exponential average in eqn (1) is strongly domi-

nated by instances in which small work values arise. Since such

instances (trajectories) occur rarely, direct application of this

equation to calculate a PMF is not practical. However, in case

the work values follow a Gaussian distribution, the cumulant

expansions of eqn (1) contributes only first and second order

terms, which permits easy calculation of the exponential

average.69 In a SMD simulation performed with a stiff spring,

the work on the system is indeed Gaussian-distributed and the

2nd order cumulant expansion of Jarzynski’s equality can be

applied.69 This method for determining the PMF compares

favorably with the widely used umbrella sampling method

because of its easy implementation and uniform sampling.70

The Jarzynski equality has been employed successfully to

reconstruct the PMF characterizing the conduction of small

molecules through channel proteins.71,72

Titin

An essential characteristic of striated muscle is its elasticity.

Tiny muscle fibrils, known as myofibrils (1–2 mm in diameter),

can be stretched to twice their resting length without damaging

their structure. At the molecular level, the elasticity is due to a

filament composed of a single gigantic protein, titin.5,6 As

shown schematically in Fig. 1, titin spans over half of the

vertebrate striated-muscle sarcomere, the smallest self-con-

tained functional unit of myofibrils. A typical titin molecule

has a length of B1 mm and a molecular weight of up to B4

MDa. In fact, titin is the largest covalently linked protein

encoded in the human genome. Sequence analysis suggests

that titin is linearly assembled from about 300 modules of two

types, immunoglobulin-like (Ig) and fibronectin type III

(FN-III), as well as a few other domains.73,74 A unique PEVK

domain (rich in proline (P), glutamate (E), valine (V), and

lysine (K)) has a flexible secondary structure,73,75 and becomes

unfolded first upon stretching.76,77 To prevent the high force

developed in sarcomere, a few individual Ig domains in the

I-band region of titin also become unfolded.78,79

The mechanical properties of titin Ig domains have been

studied by means of AFM14,21,33,79,81–83 and optical twee-

zers84,85 as well as SMD simulations.30,32,33,35,36,38,56,86 The

combination of observation and simulation revealed that titin

acts as a heterogeneous spring protected against rupture by the

ability of individual domains to partially and completely

unfold. In particular, computational modeling has provided

important insights into the design principles of proteins that

act as elastic elements and, at the same time, withstand the

considerable forces arising from cellular mechanics. A classic

example is the titin I-band Ig domain, I27 (or I91 in the new

nomenclature74). SMD simulations30,32,33,35 and AFM experi-

ments21,33,81,83 explained how the double b-sheet architectureof I27 is optimal for the desired mechanical properties—

elasticity at short extension and protection against rupture

through two-step unraveling (involving a mechanically stable

intermediate state at about 10 A extension and involving the

completely unfolded state extending to about 300 A). The

force-bearing elements of I27 are inter-strand hydrogen bonds

near the N- and C-termini; these bonds have to break con-

currently before the stretched domain can extend further, the

concerted bond breaking posing high energy barriers against

extension. Altering the number of hydrogen bonds connecting

force bearing, i.e., terminal, b-strands permitted evolution to

design domains of specific strength.

The computational work took advantage of two develop-

ments, the availability of an NMR structure of I2787 and the

rise of AFM, a methodology ideally suited for the investiga-

tion of titin domains.14,21,33,79,81–83 SMD permitted direct

comparison between simulations and AFM observations.

These simulations led to experiments of I27 mutants which

modulated the force bearing elements corroborating earlier

findings.33,88 In addition to these SMD studies employing

explicit solvents, computational studies with simplified models

Fig. 1 Schematic overview of the muscle protein titin in the muscle sarcomere. The sarcomere contains three major filaments: actin filaments,

myosin filaments, and titin filaments. The titin filaments connect to the actin filaments at the Z-disc and associate with the myosin filament over the

A-band and M-line regions. The contractile movement of the sarcomere is due to the sliding of the myosin filament over the actin filament, while

the unfolding of titin domains provide the extension for the sarcomere during stretching of the sarcomere. Note that only half of the sarcomere is

shown. Ig and FN-III domains, two common structural motifs of titin, are represented by circles and ovals, respectively. The N-terminal Z1Z2 Ig

domains of two titins (shown in blue and red circles) are connected through a protein called telethonin (yellow). The crystal structure of the

complex is shown in cartoon representation (Protein Data Bank code 1YA580).

3694 | Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 This journal is �c the Owner Societies 2006

have been reported, including an implicit solvent model89,81

and coarse-grained models.90,91

A second titin I-band Ig domain that became structurally

known is I1.92 I1 exhibits, in particular, a strong network of

ten inter-strand hydrogen bonds protecting against the exten-

sion of the domain’s termini. The strength of the protection

and the lack of an I27-like intermediate state was seen both in

AFM measurements82 and simulation.38 I1 also contains two

cysteine residues that can form a disulfide bridge in an

oxidized environment, further protecting against extension of

the protein. The simulations, comparing oxidized and reduced

I1, demonstrated that this disulfide bridge increases the me-

chanical stability and limits the extension of oxidized I1.38

This was then confirmed by AFM observation.82

One of the main surprises observed in the MD investigations

of I1 and I27 was the essential role of water in rupturing titin

domains: water molecules constantly attack and break inter-

strand hydrogen bonds. Unraveling of I1 and I27 is only

possible when a sufficient number of hydrogen bonds are

broken by surface water such that the remaining bonds can

be ruptured by the applied forces, i.e., forces need water

molecules as accomplices to unravel Ig domains.35,38 This role

of water seems to be typical in the unfolding of mechanical

proteins.

The terminal regions of a titin spring are anchored at the

Z-disc and M-line of a muscle sarcomere and interact with

numerous proteins.5,6 These titin-based complexes provide

not only structural support for the development and function

of myofibrils, but also play regulatory roles by detecting

stretching force in titin.93 A unique titin kinase at the

C-terminal region, for example, exhibits a conformational

change in response to mechanical force.55,94 At the very end

of the N-terminal region of titin, a sensor complex is formed

based on two titin Ig domains, Z1 and Z2,95 anchored through

the ligand telethonin.96–98 Biochemical characterization of

telethonin has shown that its presence, in conjunction with

titin Z1Z2, is required for progression of muscle growth.97

Point mutations to telethonin resulting in premature stop

codons have been correlated to a form of limb girdle muscular

dystrophy (type 2A),99–103 suggesting that telethonin plays a

major role in the stabilization of N-terminal titin at the Z-disc.

While binding studies have shown that titin Z1Z2 associates

with telethonin at the Z-disc, the specific arrangement of the

interaction was not known until very recently when the

structure of the N-terminal half of telethonin in complex with

titin Z1 and Z2 became available,80 as shown in Fig. 1. Unlike

typical ligand binding through insertion of the ligand into a

receptor pocket, the crystal structure revealed that the

liganded Z1Z2 domains of two separate antiparallel titin

N-termini are joined together by an N-terminal fragment of

the ligand telethonin through b-strand cross-linking (see Fig. 1

and 2), a structural motif that also appears in pathological

fibril formation.104–107 On the other hand, it is known that

b-strands can form mechanically stable b-sheets found in titin

Ig domains or fibronectin type III like modules (reported

above, and below). Naturally this raises the question: Does the

b-strand cross-linking between titin and telethonin represent a

novel ligand binding strategy that provides a mechanically

stable linkage?

This question has been addressed by all-atom SMD simula-

tions performed in order to understand the mechanical design

of the Z1Z2–telethonin complex.56 The simulations revealed

that the Z1 and Z2 domains are bound strongly to telethonin.

It turns out, in fact, that the Z1Z2–telethonin complex exhibits

significantly higher resistance to mechanical stretching forces

than titin Z1Z2 alone (see Fig. 2), suggesting that telethonin

plays a role in anchoring titin to the sarcomeric Z-disc.

Whereas previous studies have revealed that the unraveling

of the b-strands for titin Ig-domains constitutes the dominant

unfolding barrier,86 in the case of Z1Z2 in complex with

telethonin, the force peak observed corresponded to a detach-

ment of one virtually intact Z2 domain from telethonin.

The results from these simulations shed light on a key

structural strategy that the titin Z1Z2–telethonin complex

employs to yield extraordinary resistance to mechanical stress.

The major force bearing component of this complex is an

extensive intermolecular hydrogen bonding network formed

across b-strands between telethonin and Z1Z2 domains, and

not intramolecularly between b-strands of individual Z1 or Z2

domains (see Fig. 2). This shift to a stronger force bearing

interface reduces the chance of unraveling the individual Ig-

domains, thus stabilizing the complex. This example demon-

strates how b-strand cross-linking, i.e., formation of an inter-

molecular b-sheet, serves as an important mechanism, in effect

a molecular glue, for augmenting the ability of protein

complexes to resist mechanical stress.

Fibronectin and integrin

Cells are connected through a network known as the extra-

cellular matrix (ECM).10 Many cellular processes involve

interactions between the ECM and the cell. The ECM not

only connects cells together in tissues, but also guides their

movement during wound healing and embryonic development.

Furthermore, the ECM relays environmental signals to cells.

One essential component of the ECM is the protein fibronectin

that assembles into fibrils attaching cells to the ECM.108

Besides the fibrillar form, fibronectin also has a compact

non-functional soluble form circulating in blood. The trans-

formation from the compact form to the extended fibrillar

form of fibronectin, a highly regulated process termed fibrillo-

genesis, requires application of mechanical forces generated by

cells.109 As shown schematically in Fig. 3, cells bind and exert

forces on fibronectin through transmembrane receptor pro-

teins of the integrin family,9,110 which mechanically couple the

actin cytoskeleton to the ECM via an elaborate adhesion

complex.

Fibronectin fibrils exhibit salient elastic properties. Cells can

stretch FN fibrils up to four times longer than their relaxed

length.18 The mechanical responses of FN are conferred by its

multimodular structure composed predominantly of three

different repeats termed FN-I, FN-II, and FN-III. Each of

the two fibronectin subunits consists of 12 FN-I, 2 FN-II, and

15 to 17 FN-III modules, respectively. While each type I or

type II module contains a couple of disulfide bonds that cross-

link b-strands of the module, type III modules do not contain

any disulfide bond. Structurally, FN-III modules exhibit a

seven-b-stranded sandwich motif that has been found

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ubiquitously in many mammalian proteins.41,111,112 It has been

proposed that individual FN-III modules unfold to provide

the elasticity of FN fibrils.113 Consistent with this hypothesis,

experiments with dual-labeled fibronectin undergoing fluores-

cent resonance energy transfer show a marked reduction in

energy transfer for fibronectin incorporated into extracellular

matrix fibrils, supporting the notion that partial unfolding of

FN-III modules occurs during fibrillogenesis.114

In addition to providing the necessary elasticity for accom-

modating cell movement, stretching of FN-III modules can

expose buried binding sites that serve as nucleation sites for

the assembly of FN into fibrils. These buried binding sites,

called cryptic sites, presumably exist either within the FN-III

core or buried between the hinge regions of two neighboring

FN-III modules. Cryptic sites for fibrillogenesis have been

proposed to exist in FN-III1,115,116 FN-III2,

117 FN-III7,118

Fig. 2 Structure and mechanical stability of a telethonin-liganded titin Z1Z2 complex. Shown in the upper left is a schematic view of the b-strandalignment for the complex, with key force bearing hydrogen bonds shown for b-strand pairs AB and A0G of the titin Z1 and Z2 domains, and

hydrogen bonds linking the four G-strands on the Z1 and Z2 domains to b-strands on telethonin. Shown in the lower left is the force–extension

profile of the telethonin-liganded Z1Z2 complex and of an isolated Z1Z2 unit. The profile depicts the force needed in the constant velocity SMD

simulations to stretch the systems to a certain extension relative to the equilibrium length. Shown on the right are snapshots of the titin–telethonin

complex for various extensions. Comparing the force–extension profile one can see that unbinding the complex requires significantly higher force

than unfolding an isolated Z1Z2 unit. The complex shown in snapshot (A) defines the initial state before stretching at 0.05 A ps�1. (B) At extension

of 15 A, a peak force is necessary for detaching the G-strand of a Z2 from its cross-linking partner, the D-strand of telethonin. (C) The Z2 domain

becomes separated from the ligand at extension 25 A. (D) Unraveling the Z2 domain leads to further separation. Hydrogen bonds are represented

by dashed lines. Figure adapted from ref. 56.

Fig. 3 Schematic view of fibronectin bound to integrin at the cell surface. Fibronectin is a dimeric protein consisting of two identical subunits

cross-linked by disulfide bridges. One of the subunits, shown in the figure, is composed of type I (squares), type II (hexagons), and type III (ovals)

modules, as well as of a variable (V) region. An atomic NMR structure of FN-III1 (Protein Data Bank code 1OWW)41 is shown in cartoon

representation. Integrin is a heterogenous dimeric protein composed of two non-covalently associated subunits. Upon activation, integrin

undergoes conformational changes and mechanically links its extracellular ligands, such as fibronectin, to an intracellular cytoskeleton adhesion

complex, which involves dozens of proteins (e.g., talin and actin).

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FN-III9,119 FN-III10,

120 and FN-III13–15.118,121 Thermal or

chemical unfolding of these modules is associated with in-

creased binding by either FN or a 70 kDa N-terminal FN

fragment. Furthermore, a 76-residue fragment from FN-III1,

termed anastellin and obtained by cutting the protein A- and

B-strands off the N-terminus, binds to fibronectin and

promotes the formation of so-called superfibronectin with

enhanced adhesive properties.122

Despite remarkably similar tertiary structures, distinct

FN-III modules share low sequence homology, with the sequence

identity being typically less than 20%. Conversely, the se-

quence homology for the same FN-III module across multiple

species is notably higher, approximately 80–90%, suggesting

that sequence variability among modules is functionally sig-

nificant. The mechanical properties of individual FN-III

modules have been compared in single molecule AFM experi-

ments65,123–126 and in all-atom SMD simulation stu-

dies.34,37,39–42 The AFM experiments revealed varied

mechanical stability of FN-III modules. The relative order

of the observed stability is qualitatively consistent with the

prediction obtained from SMD simulations of several FN-III

modules FN-III7–10,12–14, and a FN-III module from tenas-

cin.42 The simulation results have shown that FN-III modules

can be pre-stretched with only minor changes to their tertiary

structures before encountering the major unfolding barrier,

and the mechanical stability of FN-III modules can be tuned

through substitutions of just a few key amino acids by altering

access of water molecules to inter-strand hydrogen bonds that

break early in the unfolding pathway.

More interestingly, the AFM experiments with FN-III

modules revealed that the mechanical response of FN-III1 is

markedly different from that of other FN-III modules such as

FN-III10, FN-III12, and FN-III13.65 FN-III1 exhibits a pro-

nounced mechanical intermediate during forced unfolding.

While a similar intermediate has been detected for other

FN-III modules such as FN-III10, it was observed less frequently

than that of FN-III1.60 A combination of NMR structural

analysis and molecular modeling provided a structural expla-

nation of this particular property of FN-III1.41 Homologous

to other structurally solved FN-III modules, FN-III1 consists

of two four-stranded b-sheets packed into a b-sandwich motif.

Unlike most other FN-III modules, however, FN-III1 misses

in its G-strand a well conserved proline residue among FN-III

modules. As a result, the key force-bearing inter-strand hydro-

gen bonds of the CDFG b-sheet of FN-III1 is extended. Thus,

the b-sheet becomes much more stable than the ABE b-sheet(Fig. 4). Upon tension, the weaker ABE b-sheet unravels first.The N-terminal portion of the module, the A- and B-strands,

completely extend to B100 A, three times the native length of

a typical FN-III module. This new conformation amounts to a

stable intermediate with the stronger b-sheet protected by a

cluster of inter-strand hydrogen bonds between G- and

F-strands. The extension difference between native state and

intermediate is in agreement with atomic force microscopy

unfolding experiments;65 the intermediate structure predicted

by the simulations is surprisingly close to the structure of

anastellin, the 76 N-terminal portion of FN-III1.127

Fibronectin is recognized by integrins a5b1 and aVb3.128

The primary sequence motif of fibronectin for integrin binding

is a tripeptide, Arg-Gly-Asp (RGD), located on the loop

connecting the force-bearing G- and F-strands of FN-III10.

Multiple mechanical unfolding pathways have been observed

in the SMD studies of this module because either of its two b-sheets may become unraveled first, or the sheets may become

disrupted simultaneously.34,40 In the most common pathway,

the G-strand near the C-terminus detaches from the module,

inducing a gradual shortening of the distance between the apex

of the RGD-containing loop and the module surface, which

reduces the loop’s accessibility to surface-bound integrins. The

shortening is followed by a straightening of the RGD loop

from a tight b-turn into a linear conformation which implies a

further decrease of the affinity and selectivity to integrins. In a

second pathway, FN-III10 exhibits an intermediate similar to

that observed in the simulations of FN-III1 (see above). The

RGD loop maintains its initial conformation until disruption

of this intermediate. These observations suggest that the RGD

loop is strategically located to undergo conformational

changes and constitute a mechanosensitive control of integrin

recognition.34

Besides the RGD peptide on FN-III10, FN-III9 also con-

tains a short peptide that binds to integrin a5b1. This site, aso-called synergy site located about 32 A from the RGD

peptide, acts together with the FN-III10 binding site to en-

hance integrin-mediated cell adhesion.129 An SMD study of

the FN-III9–10 tandem has shown that fibronectin–integrin

binding interactions can be affected through the change of the

relative distance between the two sites upon stretching.39 Prior

to force-induced unfolding of the modules, the simulations

revealed an intermediate state in which the synergy–RGD

distance is increased to approximately 55 A while both the

conformations of the RGD loop and the synergy site them-

selves remain unperturbed. This synergy–RGD distance is too

large for the RGD loop and the synergy site to co-bind the

Fig. 4 Stretching the FN-III1 module. The overall structure of

FN-III1 is shown in Fig. 3. SMD simulations, which started from an

NMR structure of the protein (Protein Data Bank code 1OWW),

revealed that the module consists of two b-sheets with different

mechanical strength.41 (A) The weaker ABE b- sheet (green) unravelsfirst when force is applied to the termini of the module, while (B) the

stronger CDFG b-sheet (red) still maintains its inter-strand hydrogen

bonding network. Unraveling of the A- and B-strands leads to (C) a

stable mechanical intermediate with the stronger b-sheet largely intact.Hydrophobic residues exposed in this intermediate likely bind to other

fibronectin modules, thereby enabling the self-assembly of fibronectin

molecules. Hydrogen and oxygen atoms are colored in white and

yellow, respectively. Panels (A) and (B) were adapted from ref. 41.

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same receptor molecule; they are thus functionally decoupled.

The simulations suggest that increased a5b1 binding contrib-

uted by the synergy site, and associated downstream cell

signaling events, can be turned off mechanically by stretching

the two FN-III modules.

Naturally, the binding between integrin and fibronectin

must sustain significant stress in order to transmit force

signals. Indeed, AFM experiments have found that disruption

of the a5b1–FN-III7–10 complex requires strong force.130 It has

been known for a long time that integrins recruit divalent

cations for the ligand binding purpose.131,132 Crystal struc-

tures of integrin aVb3, available recently both in the presence

and absence of a synthetic RGD ligand, provide the first

atomic view of how this integrin interacts with RGD-contain-

ing ligands.133,134 The integrin acquires three divalent metal

ions that coordinate the binding to the ligand. The Asp of the

RGD peptide establishes a direct contact with the ion located

at a site termed the metal ion dependent adhesion site

(MIDAS, Fig. 5), which is flanked by two neighboring ions

located at the ligand-associated metal binding site (LIMBS)

and the adjacent MIDAS (ADMIDAS). While the exact role

of the latter two sites is not clear, it has been shown that

ADMIDAS regulates the binding affinity to the ligand.135

Based on the crystal structure of the complex, computa-

tional modeling of the RGD-ligand unbinding process has

produced a dynamic picture of how the aVb3 complex resists

dissociation by mechanical forces.29 Consistent with the hy-

pothesis that integrin–ligand binding provides a stable me-

chanical linkage, the unbinding requires a high force

comparable to the peak force observed in the unfolding of

the strongest FN-III modules. This major force peak corre-

lates with the breaking of the contact between the Asp of the

RGD ligand and the MIDAS ion, as shown in Fig. 5. RGD

binding to integrins does not involve a deep binding pocket

that protects force-bearing contacts from attacks by free

water, but rather forms a shallow crevice at the interface

between the two subunits. A water molecule is tightly coordi-

nated to the divalent MIDAS ion, thereby blocking access of

free water molecules to the critical force-bearing interactions.

A similar scenario has been found through molecular dy-

namics simulations in the complex of anthrax toxin with its

cell surface receptor, the primary binding site of the latter also

involving a MIDAS motif.136

Proteins related to hearing and other mechanical

senses

The sense of hearing in vertebrates employs mechanically

sensitive hair cells of the inner ear that transduce weak

mechanical stimuli produced by sound into electrical sig-

nals.137 These specialized cells located in the organ of Corti,

on top of the basilar membrane of the cochlea, exhibit bundles

of stereocilia arranged in rows of increasing height. The

stereocilia become agitated in response to sound, resulting in

concerted bending of the bundle accompanied by depolariza-

tion/hyperpolarization of the corresponding hair cell.138,139

Fig. 6A and B show the current model explaining the mechan-

ism of sound transduction.7,137,140 Mechanosensitive ion chan-

nels in adjacent stereocilia are connected through a fine

filament, termed the tip link,141 as well as to the cytoskeleton.

Bending towards the tallest stereocilia induces stretching of the

tip link and opening of mechanosensitive channels, the latter

event mediated by a ‘‘gating spring’’, as suggested by measure-

ments of bundle elasticity.142,143 While the microscopic cellular

structures described are well understood, the molecular iden-

tity and corresponding elasticity of the different components

of the transduction apparatus (tip link and mechanosensitive

channels, either of which may form part of the gating spring)

remains elusive and the subject of intense research.144

Motivated by experimental evidence suggesting that the tip

link was made of cadherin-237,145,146 and the transduction

channel was likely a member of the TRP ion channel family

featuring numerous ankyrin repeats (TRPA1 and TRPN1

with up to 17 or 29 ankyrin repeats, respectively8,151–153), the

elasticity of both cadherin and ankyrin repeats was extensively

studied using SMD simulations.43 The outcome of the simula-

tions, recently corroborated by AFM experiments,154,174

showed remarkable and novel properties for both ankyrin

and cadherin, as described below. However, the role of these

proteins in hair cell mechanotransduction remains ambiguous

Fig. 5 Forced dissociation of a cyclic RGD mimetic ligand from the binding site of its receptor integrin aVb3. The two subunits of integrin aVand b3 are colored blue and purple, respectively. (A) Prior to the detachment of the ligand, the Asp of the RGD ligand contacts the MIDAS

divalent cation, coordinated by b3 and a water molecule. The water molecule blocks access of other water molecules until (B) the separation of the

Asp and the MIDAS ion, which triggers the dissociation of the ligand. Figure adapted from ref. 29.

3698 | Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 This journal is �c the Owner Societies 2006

as more recent experiments suggest that cadherin-23 is a

component of transient lateral links of hair cells, but not the

tip link.147–150 Moreover, TRPN1 is unlikely to be the trans-

duction channel in hair cells;155 TRPA1 knockout mice exhibit

normal balance and auditory response,156–158 indicating that

TRPA1 is not essential for hair cell mechanotransduction.

Although poly-ankyrin domains of TRPA1 and TRPN1

homologues are unlikely to form the hair cell gating spring

as originally suggested,7,43,159 their elastic properties may be

relevant in cold reception and mechanical nociception, as well

as in mechanotransduction by sensory neurons.160

Despite the uncertainties about the specific role of cadherin

repeats in hearing, the structural integrity of cadherin-23 is

relevant for hair-cells, as demonstrated by mutations of

CDH23 causing hereditary deafness (Usher syndromes).161,162

The mutations are indeed located in the extracellular domain

of cadherin-23, formed by 27 heterogeneous repeats which

may constitute the tip link or transient lateral links. The

protein also features a domain crossing the cell membrane,

and a domain located in the cytoplasm of the hair cell.163 Each

extracellular repeat consists of about 100 amino acids sharing

a common folding topology characterized by seven anti-

parallel b-strands tightly linked by hydrogen bonds, and a

highly conserved calcium binding motif (Fig. 6C).

The ankyrin segments of TRPA1 and TRPN1 are thought

to consist of up to 29 similar repeats, each made of 33 amino

acids.8,151,152 Ankyrin repeats occur in more than 400 human

proteins expressed in many tissues,164–167 each repeat being

made of two short antiparallel a-helices and a flexible loop

(Fig. 6D). Proteins of the ankyrin family contain up to 24

repeats, and the largest ankyrin-repeat crystallographic struc-

ture available to date involves twelve of the repeats from

human ankyrin-R; a structure with 24 repeats was extrapo-

lated from it through modeling.168 As Fig. 6D shows, adjacent

ankyrin repeats stack in parallel and feature a slight helical

curvature.168–171

The first characterization of the elastic response of cadherin

and ankyrin repeats at the molecular level was performed

using multiple SMD simulations.43 Following earlier work on

cadherin homophilic adhesion,28 the new simulations revealed

that a single cadherin domain (from C-cadherin172) is likely a

stiff element that responds to an external force by indepen-

dently unfolding its two b-sheets. The large forces required to

unfold these domains were found to depend on the presence or

absence of Ca21 ions, pointing out the role of calcium as a

structural stabilizer (Fig. 7A). A more recent study investi-

gated the dynamics of two adjacent cadherin domains from

E-cadherin and confirmed the relevance of calcium ions on the

conformational flexibility of these proteins.173 Interestingly,

residues involved in calcium binding motifs are related to

hereditary deafness,161,162 i.e., the respective mutations may

undermine the ability of the tip link or transient lateral links to

withstand large forces and/or form homophilic contacts.

In contrast, stacks of ankyrin repeats containing 12, 17, and

24 repeats were found to be flexible elements that respond to

weak forces (25–100 pN) by changing their overall curvature

and, despite two-fold elongations, keep their secondary struc-

ture intact; we refer to this property of ankyrin as ‘‘tertiary

structure elasticity’’ (see Fig. 7B). The stiffness of ankyrin

repeats observed in simulations (B5 mN m�1)43 is in excellent

agreement with the stiffness measured through AFM experi-

ments (B4 mN m�1).174

The simulations also showed that the response of ankyrin

repeats to weak forces is reversible on a nanosecond time scale.

External forces and constraints applied during stretching were

turned off, permitting the protein to relax for several nano-

seconds. During the relaxation, the end-to-end distance de-

creased considerably (by more than 40 A during 25 ns for a

system of 340 000 atoms containing the solvated 24 repeats of

human ankyrin-R) and the original curvature was recovered.43

Application of large forces on ankyrin induced detachment

and unfolding of individual repeats; we refer to this property,

spectacularly represented by titin and fibronectin (see above), as

‘‘secondary structure elasticity’’. The simulations predicted that

unfolding events can be identified as force peaks in constant-

velocity stretching or as steps in constant-force stretching,

since both force peaks and steps are separated byB95 A. Thus

the end-to-end distance of unfolded poly-ankyrin domains

could easily reach a maximum extension of B2000 A while

still conserving entropic stiffness and reversibility.43 These

theoretical predictions have also been confirmed by AFM

experiments on stacks of 6, 12 and 24 ankyrin repeats.154,174

Fig. 6 Mechanotransduction in hair cells. (A) The side view shows the stereocilia arranged in order of increasing height. Deflection of a hair cell’s

bundle induced by sound causes the stereocilia to bend and the tip links between them to tighten. (B) Mechanical coupling of hair cell ion channels.

Ion channels open in response to tension conveyed by tip links. The mechanism shown, involving a TRP type channel with an N-terminal ankyrin

segment linked to the cell’s cytoskeleton, is hypothetical. (C) Crystal structure of a single extracellular cadherin repeat. Calcium ions are shown as

spheres. Transient lateral links (not shown) or the tip link are thought to be made of at least 54 extracellular heterogeneous cadherin

repeats.7,145–150 (D) Model of 24 ankyrin repeats of human ankyrin-R. Each repeat is made of two a-helices and a short loop.

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Lac repressor

The mechanical manipulation of DNA is central to all aspects

of genetic regulation.11 Indeed, very often regulatory proteins

mechanically manipulate DNA away from its equilibrium

configuration by making DNA bend, loop, twist, and super-

coil.12 Examples of proteins or protein complexes that induce a

change in DNA structure include the histones,175 the protein

component of the invertasome,176 and the lac repressor

(LacI).177 In order to manipulate DNA, proteins need to over-

come mechanical strain arising from the DNA. Little is known

about how regulatory proteins are designed to handle the forces

stemming from DNA. In many cases, conformational changes

of DNA are known to occur in protein–DNA complexes, but

cannot be resolved in detail when changes are too large or

when the DNA becomes disordered. This is the case, in

particular, when regulatory proteins force DNA into loops.

DNA looping arises when two distant segments of DNA are

bound by a regulatory protein or protein complex. Such

looping is widely observed in gene regulation, both in pro-

karyotes11,180 and eukaryotes.181 DNA looping enhances both

the regulatory properties of the proteins and the ability of the

cell to respond to a wide range of signals.12,182 Specifically,

proteins and protein complexes involved in transcription in-

hibition employ looping to influence the initiation process by

blocking the promoter sequence, a site upstream from the

genes that the RNA polymerase recognizes before initiating

transcription.183 The regulatory proteins act at different bind-

ing sites on the DNA, some of them distant from the promo-

ter, exploiting the flexibility of DNA to bring themselves in

close proximity in order to block the promoter. Proteins in this

category include the lac repressor177 shown in Fig. 8, and the

l repressor.181

The lac repressor mentioned above regulates the function of

the lac operon in Escherichia coli, a set of genes involved in

lactose catabolism.182 Crystallographic structures of LacI

bound to its DNA binding sites were reported, but neither

of them contained the DNA loop.178,179 Therefore, it is unclear

Fig. 7 SMD simulations of cadherin and ankyrin. (A) Equilibrated crystal structure of cadherin (from Protein Data Bank 1L3W)172 (top) and

partially stretched conformation (bottom) shown in cartoon representation. Specific residues and water molecules surrounding calcium ions

(yellow spheres) are labeled and shown in licorice representation. (B) Equilibrated model of 24 ankyrin repeats of human ankyrin-R (top, 340 000

atom system, water not shown). Snapshots of the 24-repeat structure at the end of 10 ns constant-force simulations using forces of 25 and 50 pN

(middle and bottom). The 24 ankyrin repeats were constructed from Protein Data Bank 1N11.168

Fig. 8 Example of genetic regulation by the lac repressor. Shown is a schematic view of the lac operon when expressed (left) and repressed

(middle). LacI binds to two operator sites on the DNA and forms a loop with the intervening DNA. The crystallographic structure of LacI178,179 is

shown on the right (Protein Data Bank code 1Z04).188

3700 | Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 This journal is �c the Owner Societies 2006

what the mechanics of repression are, given that the resistance

of the connecting DNA loop is likely to change the structure of

LacI. A suitable method for obtaining the missing details is

molecular modeling starting from the known structural

elements.

While SMD simulations could be applied directly to the

study of muscle and hair cell protein systems involving 100 000

and 300 000 atom systems, the solvated lac repressor–DNA

complex is currently beyond the reach of all-atom simulations.

The protein by itself encompasses over 300 000 atoms when

placed in a solvent bath sufficiently large to permit function-

ally important motions. For the DNA bound to the protein at

its O1 and O3 operator sites and with a 76 bp loop between the

sites (see Fig. 8) to have sufficient solvent space to freely move

requires additional 500 000 atoms in a simulation. One also

expects that the loop dynamics naturally impeded by the

solvent is slow on the MD nanosecond time scale. In order

to avoid extremely long 800 000 atom simulations, one resorts

to a multiscale description in which the protein is described by

all-atom MD and the DNA by a well-established physical

model, the elastic rod model;185 both descriptions are linked

computationally, the DNA loop adapting instantly to the

protein, but also exerting forces on the protein.

Such a multiscale methodology53 has been developed based

on earlier work on the DNA elastic rod model.185–188 The

approach is illustrated in Fig. 9. One can discern that the MD

simulation involved the lac repressor bound to two short DNA

segments. The segments continue into the DNA loop through

the physical model that takes the segments as input (as

boundary conditions for solving a system of 13th order non-

linear differential equations) and yields as output the energe-

tically optimal loop geometry along with the forces with which

the DNA resists loop formation. Just like in an SMD simula-

tion, the forces are included in the MD description of LacI.

The elastic model accounts for the relevant properties of

DNA, i.e., intrinsic twist, bending anisotropy, and electro-

statics.185–188

The multiscale method has been applied to the LacI–DNA

complex.53 For this purpose, an all-atom model of LacI has

been built based on available crystallographic and NMR data,

which were either low in resolution or missing parts of the

protein.178,179,189 The model of LacI, shown in Fig. 8, was

reported in ref. 188.

LacI is assembled as a dimer of dimers, connected by a four-

helix bundle. Each dimer has a head group that binds to DNA.

Although binding of a single head group decreases expression,

repression is most efficient when the loop is present.190 The

available178 and modeled structure188 (see Fig. 8) both include

two 16 bp DNA segments nearly identical to the operators,

but have the DNA loop missing. A mathematical DNA model

predicted the structure of the missing loop.186,188

The DNA binding sites of LacI exhibit palindromic sym-

metry, giving rise to four possible binding orientations of

DNA referred to as II, IO, OI, OO (see Fig. 9), two of which

(II, OO) are equivalent when the sequence of the DNA in the

loop is not considered. This gives rise to three different loop

topologies represented also in Fig. 9. The generally accepted

loop topology is IO178,191 which is also the one simulated in

ref. 44. However, there is no conclusive data excluding the

other topologies. The structure of the DNA loop for all

topologies was obtained from the boundary conditions of

the all-atom system.53 Based on the energetics of the DNA

loops, the II/OO loop also appears a feasible candidate for the

topology of the loop in vivo.

The results of the multiscale simulations of the IO loop–

LacI construct corrected a long held view of the mechanism of

LacI. While it was assumed previously that a hinge-like

massive motion between the dimers controlled the ability of

LacI to enforce the DNA loop, the simulations suggest that

the ability of LacI to maintain the DNA in a looped config-

uration is actually due to the extreme flexibility of its head

groups (DNA binding domains) connected to the rest of the

protein through flexible linkers, while the dimers are essen-

tially immobile with respect to each other. This is illustrated in

Fig. 10 showing the head groups rotation and loop dynamics

along with a moment of inertia of the LacI head group. The

structure of the loop itself relaxed during the simulation,

showing an energy drop from B20 kBT to 12 kBT.44 Interest-

ingly, the computationally modeled behavior is in perfect

agreement with experimental data, even though those same

Fig. 9 Simulation of the lac repressor–DNA complex. (A) Setup of

the multiscale simulation: all-atom structure of the complex between

LacI and DNA in a bath of water and ions; the 75 bp-long DNA loop

connecting the protein-bound DNA segments is modeled as an elastic

ribbon; the forces of interaction between the loop and the protein-

bound DNA segments (see arrows) are included in the MD simulation.

(B) All-atom structure of the lacI–DNA complex. (C) Alternative

topologies of the DNA loop formed by LacI based on orientation of

the operators in the head groups. I denotes the 50–30 direction pointing

toward inside the protein, and O denotes the 50–30 direction pointing

away from the other head group. Notation adopted from ref. 184. The

II and OO topologies are equivalent in our model that neglects a

sequence dependence of DNA elastic properties.

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data were interpreted differently before. Edelman and colla-

borators191 have determined the distance between fluoro-

phores attached to the DNA loop near the LacI head groups

to be 50 A larger than the same distance in the crystal

structure;178 this was ascribed to an opening of the LacI cleft

when LacI actually binds to a DNA loop, which it does not in

the crystal.178,179 However, as shown in Fig. 10 the corre-

sponding increase in distance by 52 A measured in the

simulation also explains the experimental observation without

invoking a significant opening of the cleft.

Another multiscale simulation that forced LacI to open by

applying external forces to the outer DNA ends, mimicking

single molecule experiments,192–194 revealed details of the

mechanism of repression: when LacI is subject to strain from

the DNA loop, a ‘‘lock’’ mechanism kicks in and prevents the

cleft from opening. The locking mainly involves three groups

of protein residues, that account for 80% of the dimer-to-

dimer interaction energy. The interaction is mainly electro-

static, involving the formation of two salt bridges when the

protein is subject to strain and locking it through a ‘‘catch-

bond’’.195

As pointed out already, the DNA loop of the LacI–DNA

complex can, in principle, also assume alternative topologies

as shown in Fig. 9. The structure and energies of the OI and

II/OO loops have been calculated.53 The calculations show

that the energy of the II/OO loop is comparable to that of the

IO loop, while the OI loop appears energetically unfavorable

in the LacI conformation tested. Investigation of the dynamics

of the loops and the response of the protein to the respective

forces will answer the question if the alternative loops are

feasible. Given the wide rotational flexibility of LacI’s head

groups (see above), the differences in loop topology may be

irrelevant since, through head group twists, one loop

form, e.g., IO, can be transformed approximately into another

one, e.g., II.

Outlook

The living state of a biological cell manifests itself through

mechanical motion on many length scales. Behind this motion

are many processes that generate and transform mechanical

forces of many types. As with other cell functions, the ma-

chinery for cellular mechanics involves proteins. Their flexible

structures, which can be deformed and restored, are often

essential for their functions. In this review we considered a few

mechanical proteins and demonstrated what had been learned

about them through computational modeling. Regarding the

examples given we now describe what the future may hold in

store.

A few mechanical proteins take their flexibility to extremes

by unfolding part of their structures. Examples reviewed here

are the giant protein titin, the extracellular matrix protein

fibronectin, and the repeat protein ankyrin. These molecular

springs exhibit elasticity that come from their modular de-

signs. The proteins respond to weak force by straightening the

linker regions between modules. The ensuing elasticity is

conferred by re-arrangement of the tertiary structure, and is

called tertiary structure elasticity. Under strong force, indivi-

dual modules unravel, unfolding secondary structure. The

corresponding property is termed secondary structure elasti-

city. A typical structural motif for modules with secondary

structure elasticity is the b-sandwich motif found in titin and

fibronectin. The motif shows how mechanical proteins derive

their mechanical strength, i.e., resistance to unraveling under

stretching through an interstrand hydrogen-bond network.

The b-sandwich is one of the most abundant protein

structure motifs. The ground-breaking AFM experiments

and SMD simulations of titin Ig domains and fibronectin type

III modules have revealed a general mechanism for how a

typical b-sandwich protein resists mechanical force: b-strandsformed in the terminal regions of the protein are typically

crucial force-bearing elements. The mechanical strength of

individual b-sandwich modules can be tuned through varia-

tion of amino acids in these key b-strands. Moreover, some b-sandwich proteins, such as FN-III modules, exhibit stable

mechanical intermediates that adhere to each other to form

fibrils. Although it is not clear precisely how these modules

cross-link, one possible way involves b-strand cross-linking.119

As revealed in the structure and simulations of the titin

Z1Z2–telethonin complex, b-strand cross-linking is a funda-

mental architectural element used by cells to glue their mole-

cular components together yielding strong mechanical

Fig. 10 LacI head group and DNA loop motion during the multiscale simulation. The protein structure is shown before and after the simulation.

The lines in (A) represent the long principal axis of each head group after every 200 ps of the simulation. The structure of the DNA loop in (B) is

drawn with the same frequency. (C) The distance d between two fluorophores attached to the DNA loop in ref. 191. Ddtotal shows the change in d

during the simulation; Dda shows how d would change if the head groups were immobile with respect to the core domains. The mauve band with

the dotted line shows the experimental range and the average estimated for d.191 Figure adapted from ref. 44.

3702 | Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 This journal is �c the Owner Societies 2006

connections. This structural motif has also been implicated in

pathological fibril formation.196 Clearly, the deployment of

fibronectin, telethonin, and other similar mechanical proteins

as powerful glue needs to be carefully controlled in the cell and

future work will likely focus on the control mechanisms used

in gluing the right protein components, and not the wrong

ones, avoiding, in particular, self-aggregation.

Integrins, signaling receptor proteins, are vital players in-

volved in transducing mechanical force signals across the cell

membrane between the intracellular cytoskeleton complex and

the extracellular matrix. Maintaining a stable mechanical

linkage between integrins and their extracellular matrix

ligands, as demonstrated in SMD simulations, is important

for mechanotransduction. Furthermore, inactivated integrins,

namely, the receptors in the absence of bound ligands, may be

activated by mechanical force exerted on the cytoplasmic tails

of integrins, opening sites that bind to the receptors.9 Such

force signals trigger conformational changes cascading to the

integrin headpiece,197–199 thus activating the receptors. The

essential structural components of integrins for relaying and

regulating conformational changes and cellular signaling are

still not clearly understood.

Repeat proteins such as ankyrin are recognized today as

ubiquitous components of biological cells. Examples are pro-

teins made of leucine-rich repeats (LRR), armadillo repeats,

and heat repeats like internalin, decorin, importin-b, exportin,clathrin, or catenin. These proteins resemble in a striking

manner the overall curved architecture of ankyrin and likely

exhibit secondary and tertiary structure elasticity similar to

those of ankyrin. Do these repeat proteins have mechanical

functions? If they do, how do their elastic properties serve their

functions? One interesting case is the leucine rich repeat (LRR)

domain of internalin from the bacterium Listeria monocyto-

genes.200 The bacterium utilizes the rubber-band-like LRR

domain to grip firmly a cellular receptor, E-cadherin, on the

surface of a host cell. For such a system, SMD simulations

provide a viable means to probe the elasticity of the structure

and investigate how uncurling the LRR domain may affect the

binding strength to its receptor. Another interesting example

of repeat proteins with mechanical function are transport

receptors associated with the nuclear pore complex.201 The

transport receptors embrace cargos, deliver them across the

nuclear pore, and release them. The recognition of the trans-

port receptor importin-b and transport factor NTF2 by

nuclear pore complex proteins has been reported re-

cently.202,203 The mechanical flexibility of the transport recep-

tors is thought to be important for its function and is under

investigation.

The lac repressor is a paradigm of genetic control;177 its

ability to bind DNA and regulate gene expression is common

to many regulatory proteins across all biological king-

doms.11,12 The mechanisms by which LacI can arrest DNA

into a looped configuration is a remarkable example of protein

mechanics, in which a protein has to withstand large mechan-

ical strain arising from forcing DNA into a looped configura-

tion. Multiscale simulations have revealed which mechanical

degrees of freedom are relevant to this task, allowing one to

understand the underlying design of this class of proteins

consisting of DNA binding domains linked by flexible linkers

to large protein cores.204 The multiscale method can be used to

study all possible DNA loop topologies induced by these

regulatory proteins, besides that of LacI, also that of the gal

repressor, another E. coli regulator that supposedly forms an

antiparallel, i.e., II/OO loop.205 Future work will study the

feasibility of these alternative topologies, characterize their

properties, and asses the possibility of dynamical exchange

between them.

Acknowledgements

The work reviewed here involved many members of our

research group. We would like to thank Alexander Balaeff,

Paul Grayson, Justin Gullingsrud, Barry Isralewitz, Sergei

Izrailev, Hui Lu, and Sanghyun Park for their contributions

and insightful suggestions. The authors are grateful to their

long-time collaborator, Viola Vogel, for guidance and inspira-

tions, as well as collaborators David Corey, David Craig,

Andre Krammer, and Matthias Wilmanns. We also thank

Julio Fernandez and Piotr Marszalek for a wonderful experi-

mental–theoretical collaboration. Our work was supported by

the National Institutes of Health (NIH PHS-5-P41-RR05969

and NIH R01-GM073655). Computer time was provided

through the National Resource Allocation Committee grant

(NRACMCA93S028) from the National Science Foundation.

All molecular graphic figures were generated with VMD.206

References

1 J. Howard, Mechanics of Motor Proteins and the Cytoskeleton,Sinauer Associates, Inc., Sunderland, MA, 2001.

2 P. D. Boyer, Annu. Rev. Biochem., 1997, 66, 717–749.3 M. Yoshida, E. Muneyuki and T. Hisabori, Nat. Rev. Mol. CellBiol., 2001, 2, 669–677.

4 O. P. Hamill and B. Martinac, Physiol. Rev., 2001, 81(2),685–740.

5 L. Tskhovrebova and J. Trinick, Nat. Rev. Mol. Cell Biol., 2003,4(9), 679–689.

6 H. L. Granzier and S. Labeit, Circ. Res., 2004, 94, 284–295.7 D. P. Corey and M. Sotomayor, Nature, 2004, 428, 901–902.8 D. P. Corey, J. Garcıa-Anoveros, J. R. Holt, K. Y. Kwan, S. Lin,M. A. Vollrath, A. Amalfitano, E. L.-M. Cheung, B. H. Derfler,D. A., G. S. G. Geleoc, P. A. Gray, M. P. Hoffman, H. L. Rehm,D. Tamasauskas and D. Zhang, Nature, 2004, 432, 723–730.

9 R. O. Hynes, Cell, 2002, 110, 673–687.10 B. Geiger, A. Bershadsky, R. Pankov and K. Yamada, Nat. Rev.

Mol. Cell Biol., 2001, 2, 793–805.11 R. Schleif, Annu. Rev. Biochem., 1992, 61, 199–223.12 K. S. Matthews, Microbiol. Rev., 1992, 56(1), 123–136.13 E.-L. Florin, V. T. Moy and H. E. Gaub, Science, 1994, 264,

415–417.14 M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandez and H. E.

Gaub, Science, 1997, 276, 1109–1112.15 K. Svoboda, C. Schmidt, B. Schnapp and S. Block, Nature, 1993,

365, 721–727.16 S. B. Smith, Y. Cui and C. Bustamante, Science, 1996, 271,

795–799.17 T. Ha, X. W. Zhuang, H. D. Kim, J. W. Orr, J. R. Williamson

and S. Chu, Proc. Natl. Acad. Sci. U. S. A., 1999, 96(16),9077–9082.

18 T. Ohashi, D. P. Kiehart and H. P. Erickson, Proc. Natl. Acad.Sci. U. S. A., 1999, 96, 2153–2158.

19 A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldmanand P. R. Selvin, Science, 2003, 300(5628), 2061–2065.

20 R. Merkel, P. Nassoy, A. Leung, K. Ritchie and E. Evans,Nature, 1999, 397, 50–53.

This journal is �c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 | 3703

21 M. Carrion-Vazquez, A. Oberhauser, S. Fowler, P. Marszalek, S.Broedel, J. Clarke and J. Fernandez, Proc. Natl. Acad. Sci. U. S.A., 1999, 96, 3694–3699.

22 S. Izrailev, S. Stepaniants, M. Balsera, Y. Oono and K. Schulten,Biophys. J., 1997, 72, 1568–1581.

23 B. Isralewitz, S. Izrailev and K. Schulten, Biophys. J., 1997, 73,2972–2979.

24 W. Wriggers and K. Schulten, Proteins: Struct., Funct., Genet.,1999, 35, 262–273.

25 D. Kosztin, S. Izrailev and K. Schulten, Biophys. J., 1999, 76,188–197.

26 S. Izrailev, S. Stepaniants, B. Isralewitz, D. Kosztin, H. Lu, F.Molnar, W. Wriggers and K. Schulten, in Computational Mole-cular Dynamics: Challenges, Methods, Ideas, ed. P. Deuflhard, J.Hermans, B. Leimkuhler, A. E. Mark, S. Reich and R. D. Skeel,vol. 4 of Lecture Notes in Computational Science and Engineer-ing, Springer-Verlag, Berlin, 1998, pp. 39–65.

27 M. V. Bayas, K. Schulten and D. Leckband, Biophys. J., 2003, 84,2223–2233.

28 M. V. Bayas, K. Schulten and D. Leckband, Mech. Chem.Biosystems, 2004, 1, 101–111.

29 D. Craig, M. Gao, K. Schulten and V. Vogel, Structure, 2004, 12,2049–2058.

30 H. Lu, B. Isralewitz, A. Krammer, V. Vogel and K. Schulten,Biophys. J., 1998, 75, 662–671.

31 H. Lu and K. Schulten, Proteins: Struct., Funct., Genet., 1999, 35,453–463.

32 H. Lu and K. Schulten, Chem. Phys., 1999, 247, 141–153.33 P. E. Marszalek, H. Lu, H. Li, M. Carrion-Vazquez, A. F.

Oberhauser, K. Schulten and J. M. Fernandez, Nature, 1999,402, 100–103.

34 A. Krammer, H. Lu, B. Isralewitz, K. Schulten and V. Vogel,Proc. Natl. Acad. Sci. U. S. A., 1999, 96, 1351–1356.

35 H. Lu and K. Schulten, Biophys. J., 2000, 79, 51–65.36 M. Gao, H. Lu and K. Schulten, Biophys. J., 2001, 81, 2268–2277.37 D. Craig, A. Krammer, K. Schulten and V. Vogel, Proc. Natl.

Acad. Sci. U. S. A., 2001, 98, 5590–5595.38 M. Gao, M. Wilmanns and K. Schulten, Biophys. J., 2002, 83,

3435–3445.39 A. Krammer, D. Craig, W. E. Thomas, K. Schulten and V. Vogel,

Matrix Biol., 2002, 21, 139–147.40 M. Gao, D. Craig, V. Vogel and K. Schulten, J. Mol. Biol., 2002,

323, 939–950.41 M. Gao, D. Craig, O. Lequin, I. D. Campbell, V. Vogel and K.

Schulten, Proc. Natl. Acad. Sci. U. S. A., 2003, 100, 14784–14789.42 D. Craig, M. Gao, K. Schulten and V. Vogel, Structure, 2004, 12,

21–30.43 M. Sotomayor, D. P. Corey and K. Schulten, Structure, 2005, 13,

669–682.44 E. Villa, A. Balaeff and K. Schulten, Proc. Natl. Acad. Sci. U. S.

A., 2005, 102, 6783–6788.45 S. Izrailev, A. R. Crofts, E. A. Berry and K. Schulten, Biophys. J.,

1999, 77, 1753–1768.46 B. Isralewitz, J. Baudry, J. Gullingsrud, D. Kosztin and K.

Schulten, J. Mol. Graphics Modell., 2001, 19, 13–25.47 B. Isralewitz, M. Gao and K. Schulten, Curr.Opin. Struct. Biol.,

2001, 11, 224–230.48 H. Grubmuller, B. Heymann and P. Tavan, Science, 1996, 271,

997–999.49 A. Aksimentiev, I. A. Balabin, R. H. Fillingame and K. Schulten,

Biophys. J., 2004, 86, 1332–1344.50 I. Kosztin, R. Bruinsma, P. O’Lague and K. Schulten, Proc. Natl.

Acad. Sci. U. S. A., 2002, 99, 3575–3580.51 J. Gullingsrud, D. Kosztin and K. Schulten, Biophys. J., 2001, 80,

2074–2081.52 M. Sotomayor and K. Schulten, Biophys. J., 2004, 87, 3050–3065.53 E. Villa, A. Balaeff, L. Mahadevan and K. Schulten, Multiscale

Model. Simul., 2004, 2, 527–553.54 E. Paci and M. Karplus, J. Mol. Biol., 1999, 288, 441–459.55 F. Grater, J. Shen, H. Jiang, M. Gautel and H. Grubmuller,

Biophys. J., 2005, 88, 790–804.56 E. H. Lee, M. Gao, N. Pinotsis, M. Wilmanns and K. Schulten,

Structure, 2006, 14, 497–509.57 P. Grayson, E. Tajkhorshid and K. Schulten, Biophys. J., 2003,

85, 36–48.

58 J. Stone, J. Gullingsrud, P. Grayson and K. Schulten, in ACMSymposium on Interactive 3D Graphics, ed. J. F. Hughes and C. H.Sequin, New York, 2001, pp. 191–194, ACM SIGGRAPH.

59 J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid,E. Villa, C. Chipot, R. D. Skeel, L. Kale and K. Schulten, J.Comput. Chem., 2005, 26, 1781–1802.

60 L. Li, H. H. Huang, C. L. Badilla and J. M. Fernandez, J. Mol.Biol., 2005, 345, 817–826.

61 J. Gullingsrud, R. Braun and K. Schulten, J. Comput. Phys.,1999, 151, 190–211.

62 K. Schulten, Z. Schulten and A. Szabo, Physica A, 1980, 100,599–614.

63 A. Szabo, K. Schulten and Z. Schulten, J. Chem. Phys., 1980, 72,4350–4357.

64 K. Schulten, Z. Schulten and A. Szabo, J. Chem. Phys., 1981, 74,4426–4432.

65 A. Oberhauser, C. Badilla-Fernandez, M. Carrion-Vazquez andJ. Fernandez, J. Mol. Biol., 2002, 319, 433–447.

66 C. Jarzynski, Phys. Rev. Lett., 1997, 78, 2690–2693.67 C. Jarzynski, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat.

Interdiscip. Top., 1997, 56, 5018–5035.68 G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. U. S. A., 2001,

98, 3658–3661.69 S. Park and K. Schulten, J. Chem. Phys., 2004, 120, 5946–5961.70 S. Park, K. Khalidi-Araghi, E. Tajkhorshid and K. Schulten, J.

Chem. Phys., 2003, 119, 3559–3566.71 M. Ø. Jensen, S. Park, E. Tajkhorshid and K. Schulten, Proc.

Natl. Acad. Sci. U. S. A., 2002, 99, 6731–6736.72 Y. Wang, K. Schulten and E. Tajkhorshid, Structure, 2005, 13,

1107–1118.73 S. Labeit and B. Kolmerer, Science, 1995, 270, 293–296.74 M. L. Bang, T. Centner, F. Fornoff, A. J. Geach, M. Gotthardt,

M. McNabb, C. C. Witt, D. Labeit, C. C. Gregorio, H. Granzierand S. Labeit, Circ. Res., 2001, 89(11), 1065–1072.

75 K. Ma, L. S. Kan and K. Wang, Biochemistry, 2001, 40(12),3427–3438.

76 W. A. Linke, M. Ivemeyer, P. Mundel, M. R. Stockmeier and B.Kolmerer, Proc. Natl. Acad. Sci. U. S. A., 1998, 95(14),8052–8057.

77 H. B. Li, A. F. Oberhauser, S. D. Redick, M. Carrion-Vazquez,H. P. Erickson and J. M. Fernandez, Proc. Natl. Acad. Sci. U. S.A., 2001, 98(19), 10682–10686.

78 A. Minajeva, M. Kulke, J. M. Fernandez and W. A. Linke,Biophys. J., 2001, 80, 1442–1451.

79 H. Li, W. Linke, A. F. Oberhauser, M. Carrion-Vazquez, J. G.Kerkvliet, H. Lu, P. E. Marszalek and J. M. Fernandez, Nature,2002, 418, 998–1002.

80 P. J. Zou, N. Pinotsis, M. Marino, S. Lange, A. Popov, I.Mavridis, M. Gautel, O. M. Mayans and M. Wilmanns, Nature,2006, 439, 229–233.

81 S. B. Fowler, R. B. Best, J. L. T. Herrera, T. J. Rutherford, A.Steward, E. Paci, M. Karplus and J. Clarke, J. Mol. Biol., 2002,322(4), 841–849.

82 H. B. Li and J. M. Fernandez, J. Mol. Biol., 2003, 334(1), 75–86.83 P. M. Williams, S. B. Fowler, R. B. Best, J. L. Toca-Herrera, K.

A. Scott, A. Steward and J. Clarke, Nature, 2003, 422(6930),446–449.

84 M. Kellermayer, S. Smith, H. Granzier and C. Bustamante,Science, 1997, 276, 1112–1116.

85 L. Tskhovrebova, J. Trinick, J. Sleep and R. Simmons, Nature,1997, 387, 308–312.

86 M. Gao, H. Lu and K. Schulten, J. Muscle Res. Cell Motil., 2002,23, 513–521.

87 S. Improta, A. Politou and A. Pastore, Structure, 1996, 4,323–337.

88 H. Li, C. V. Mariano, A. F. Oberhauser, P. E. Marszalek and J.M. Fernandez, Nat. Struct. Biol., 2001, 7, 1117–1120.

89 E. Paci and M. Karplus, Proc. Natl. Acad. Sci. U. S. A., 2000, 97,6521–6526.

90 D. K. Klimov and D. Thirumalai, Proc. Natl. Acad. Sci. U. S. A.,1999, 96, 1306–1315.

91 M. Cieplak, T. X. Hoang and M. O. Robbins, Proteins: Struct.,Funct., Genet., 2002, 49(1), 114–124.

92 O. Mayans, J. Wuerges, S. Canela, M. Gautel and M. Wilmanns,Structure, 2001, 9, 331–340.

3704 | Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 This journal is �c the Owner Societies 2006

93 M. Miller, H. Granzier, E. Ehler and C. Gregorio, Trends CellBiol., 2004, 14, 119–126.

94 S. Lange, F. Xiang, A. Yakovenko, A. Vihola, P. Hackman, E.Rostkova, J. Kristensen, B. Brandmeier, G. Franzen, B. Hedberg,L. Gunnarsson, S. Hughes, S. Marchand, T. Sejersen, I. Richard,L. Edstrom, B. Udd and M. Gautel, Science, 2005, 308,1599–1603.

95 R. Knoll, M. Hoshijima, H. Hoffman, V. Person, I. Lorenzen-Schmidt, M. Bang, T. Hayashi, N. Shiga, H. Yasukawa, W.Schaper, W. McKenna, M. Yokoyama, N. Schork, H. Omens,A. McCulloch, A. Kimura, C. Gregorio, W. Poller, J. Schaper, H.Schultheiss and K. Chien, Cell, 2002, 111, 943–955.

96 G. Valle, G. Faulkner, A. DeAntoni, P. Pacchioni, A. Pallavicini,D. Pandolfo, N. Tiso, S. Toppo, S. Trevisan and G. Lanfranchi,FEBS Lett., 1997, 415, 163–168.

97 C. C. Gregorio, K. Trombitas, T. Centner, B. Kolmerer, G. Stier,K. Kunke, K. Suzuki, F. Obermayr, B. Herrmann, H. Granzier,H. Sorimachi and S. Labeit, J. Cell Biol., 1998, 143(4),1013–1027.

98 G. Faulkner, G. Lanfranchi and G. Valle, Life, 2001, 51, 275–282.99 R. Schroder, J. Reimann, A. Iakovenko, A. Mues, C. Bonne-

mann, J. Matten and M. Gautel, J. Muscle Res. Cell Motil., 2001,22, 259–264.

100 M. Itoh-Satoh, T. Hayashi, H. Nishi, Y. Koga, T. Arimura, T.Koyanagi, M. Takahashi, S. Hohda, K. Ueda, T. Nouchi, M.Hiroe, F. Marumo, T. Imaizumi, M. Yasunami and A. Kimura,Biochem. Biophys. Res. Commun., 2002, 291(2), 385–393.

101 M. Vainzof, E. Moreira, O. Suzuki, G. Faulkner, G. Valle, A.Beggs, O. Carpen, A. Ribeiro, E. Zanoteli, J. Gurgel-Gianneti, A.M. Tsanaclis, H. Silva, M. R. Passos-Bueno and M. Zatz,Biochim. Biophys. Acta, 2002, 1588, 33–40.

102 C. Bonnemann and N. Laing, Curr. Opin. Neurol., 2004, 17,529–537.

103 S. Laval and K. Bushby, Neuropathol. Appl. Neurobiol., 2004, 30,91–105.

104 L. Tjernberg, D. Callaway, A. Tjernberg, S. Hahne, C. Lillie-hook, L. Terenius, J. Thyberg and C. Nordstedt, J. Biol. Chem.,1999, 274, 12619–12625.

105 D. Walsh, D. Hartley, M. Condron, M. Selkoe and D. Teplow,Biochem. J., 2001, 355, 869–877.

106 J. Karanicolas and C. Brooks, Proc. Natl. Acad. Sci. U. S. A.,2003, 100, 3555–3556.

107 J. Wang, S. Gulich, C. Bradford, M. Ramirez-Avarado and L.Regan, Structure, 2005, 13, 1279–1288.

108 R. O. Hynes, Fibronectins, Springer-Verlag, New York, 1990.109 Y. Mao and J. E. Schwarzbauer, Matrix Biol., 2005, 24(6),

389–399.110 M. Shimaoka, J. Takagi and T. A. Springer, Annu. Rev. Biophys.

Biomol. Struct., 2002, 31, 485–516.111 D. J. Leahy, I. Aukhil and H. P. Erickson, Cell, 1996, 84,

155–164.112 A. Sharma, J. A. Askari, M. J. Humphries, E. Y. Jones and D. I.

Stuart, EMBO J., 1999, 18, 1468–1479.113 H. Erickson, Proc. Natl. Acad. Sci. U. S. A., 1994, 91,

10114–10118.114 G. Baneyx, L. Baugh and V. Vogel, Proc. Natl. Acad. Sci. U. S.

A., 2002, 99, 5139–43.115 D. C. Hocking, J. Sottile and P. J. McKeown-Longo, J. Biol.

Chem., 1994, 269, 19183–19187.116 D. C. Hocking and K. Kowalski, J. Cell Biol., 2002, 158(1),

175–84.117 J. L. Sechler, H. Rao, A. Cumiskey, I. Vega-Colon, M. Smith, T.

Murata and J. Schwarzbauer, J. Cell Biol., 2001, 154, 1081–8.118 K. C. Ingham, S. Brew, S. Huff and S. Litvinovich, J. Cell

Biochem., 1997, 272, 1718–24.119 S. V. Litvinovich, S. Brew, S. Aota, S. Akiyama, C. Haudenschild

and K. Ingham, J. Mol. Biol., 1998, 280, 245–58.120 D. C. Hocking, R. K. Smith and P. J. McKeown-Longo, J. Cell

Biol., 1996, 133, 431–444.121 H. Bultmann, A. Santas and D. Peters, J. Biol. Chem., 1998, 273,

2601–9.122 A. Morla, Z. Zhang and E. Ruoslahti, Nature, 1994, 367(6459),

193–6.123 A. F. Oberhauser, P. E. Marszalek, H. Erickson and J. Fernan-

dez, Nature, 1998, 393, 181–185.

124 M. Rief, M. Gautel, A. Schemmel and H. Gaub, Biophys. J.,1998, 75, 3008–3014.

125 Y. Oberdorfer, H. Fuchs and A. Janshoff, Langmuir, 2000, 16,9955–9958.

126 S. P. Ng, R. W. S. Rounsevell, A. Steward, C. D. Geierhaas, P.M. Williams, E. Paci and J. Clarke, J. Mol. Biol., 2005, 350(4),776–789.

127 K. Briknarova, M. E. Akerman, D. W. Hoyt, E. Ruoslahti and K.R. Ely, J. Mol. Biol., 2003, 332(1), 205–15.

128 E. Ruoslahti, Annu. Rev. Cell Dev. Biol., 1996, 12, 697–715.129 R. P. Grant, C. Spitzfaden, H. Altroff, I. D. Campbell and H. J.

Mardon, J. Biol. Chem., 1997, 272(10), 6159–6166.130 F. Y. Li, S. D. Redick, H. P. Erickson and V. T. Moy, Biophys. J.,

2003, 84(2), 1252–1262.131 J. W. Lee, F. Ryan, J. C. Swaffield, S. A. Johnston and D. D.

Moore, Nature, 1995, 374, 91–94.132 J. Emsley, C. G. Knight, R. W. Farndale, M. J. Barnes and R. C.

Liddington, Cell, 2000, 101(1), 47–56.133 J. P. Xiong, T. Stehle, B. Diefenbach, R. Zhang, R. Dunker, D. L.

Scott, A. Joachimiak, S. L. Goodman and M. A. Arnaout,Science, 2001, 294, 339–345.

134 J. P. Xiong, T. Stehle, R. Zhang, A. Joachimiak, M. Frech, S. L.Goodman and M. A. Arnaout, Science, 2002, 296, 151–155.

135 A. P. Mould, S. J. Barton, J. A. Askari, S. E. Craig and M. J.Humphries, J. Biol. Chem., 2003, 278(51), 51622–51629.

136 M. Gao and K. Schulten, Biophys. J., 2006, 90, 3267–3279.137 P. G. Gillespie and R. G. Walker, Nature, 2001, 413, 194–202.138 A. J. Hudspeth and D. P. Corey, Proc. Natl. Acad. Sci. U. S. A.,

1977, 74, 2407–2411.139 D. P. Corey and A. J. Hudspeth, J. Neurosci., 1983, 3, 962–976.140 E. Perozo, Nat. Rev. Mol. Cell Biol., 2006, 7, 109–119.141 J. O. Pickles, S. D. Comis and M. P. Osborne, Hear. Res., 1984,

15, 103–112.142 J. Howard and A. J. Hudspeth, Neuron, 1988, 1, 189–199.143 E. L. Cheung and D. P. Corey, Biophys. J., 2005, 90, 124–139.144 P. G. Gillespie, R. A. Dumont and B. Kachar, Curr. Opin.

Neurol., 2005, 15, 389–396.145 J. Siemens, C. Lillo, R. A. Dumont, A. Reynolds, D. S. Williams,

P. G. Gillespie and U. Muller, Nature, 2004, 428, 950–955.146 C. Sollner, G.-J. Rauch, J. Siemens, R. Geisler, S. C. Schuster, U.

Muller and T. Nicolson, The Tubingen 2000 Screen Consortium,Nature, 2004, 428, 955–958.

147 V. Tsuprun, R. J. Goodyear and G. P. Richardson, Biophys. J.,2004, 87, 4106–4112.

148 A. K. Rzadzinska, A. Derr, B. Kachar and K. Noben-Trauth,Hear. Res., 2005, 208, 114–121.

149 A. Lagziel, Z. M. Ahmed, J. M. Schultz, R. J. Morell, I. A.Belyantseva and T. B. Friedman, Dev. Biol., 2005, 280, 295–306.

150 V. Michel, R. J. Goodyear, D. Weil, W. Marcotti, I. Perfettini, U.Wolfrum, C. J. Kros, G. P. Richardson and C. Petit, Dev. Biol.,2005, 280, 281–294.

151 R. G. Walker, A. T. Willingham and C. S. Zuker, Science, 2000,287, 2229–2234.

152 S. Sidi, R. W. Friederich and T. Nicolson, Science, 2003, 301,96–99.

153 K. Nagata, A. Duggan, G. Kumar and J. Garcı a Anoveros, J.Neurosci., 2005, 25, 4052–4061.

154 L. Li, S. Wetzel, A. Pluckthun and J. M. Fernandez, Biophys. J.,2006, 90, L30–L32.

155 J. Shin, D. Adams, M. Paukert, M. Siba, S. Sidi, M. Levin, P. G.Gillespie and S. Grunder, Proc. Natl. Acad. Sci. U. S. A., 2005,102, 12572–12577.

156 K. Y. Kwan, A. J. Allchorne, M. A. Vollrath, A. P. Christensen,D. S. Zhang, C. J. Woolf and D. P. Corey, Neuron, 2006, 50,277–289.

157 D. Bautista, S. E. Jordt, T. Nikai, P. R. Tsuruda, A. J. Read, E.N. Poblete, J. Yamoah, A. I. Basbaum and D. Julius, Cell, 2006,124, 1269–1282.

158 G. M. Story and R. W. Gereau, Neuron, 2006, 50, 177–180.159 J. Howard and S. Bechstedt, Curr. Biol., 2004, 14, 224–226.160 W. Li, Z. Feng, P. W. Sternberg and X. Z. S. Xu, Nature, 2006,

440, 684–687.161 J. M. Bork, L. M. Peters, S. Riazuddin, S. L. Bernstein, Z. M.

Ahmed, S. L. Ness, R. Polomeno, A. Ramesh, M. Schloss, C. R.S. Srisailpathy, D. Desmukh, Z. Ahmed, S. N. Khan, V. M. der

This journal is �c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 3692–3706 | 3705

Kaloustian, X. C. Li, A. Lalwani, S. Riazuddin, M. Bitner-Glindzicz, W. E. Nance, X.-Z. Liu, G. Wistow, R. J. H. Smith,A. J. Griffith, E. R. Wilcox, T. B. Friedman and R. J. Morell, Am.J. Hum. Genet., 2001, 68, 26–37.

162 A. P. M. de Brouwer, R. J. Pennings, M. Roeters, P. van Hauwe,L. M. Astuto, L. H. Hoefsloot, P. L. M. Huygen, B. van denhelm, A. F. Deutman, J. M. Bork, W. J. Kimberling, F. P. M.Cremers, C. W. R. J. Cremers and H. Kremer,Hum. Genet., 2003,112, 156–163.

163 F. Di Palma, R. Pellegrino and K. Noben-Trauth, Gene, 2001,281, 31–41.

164 S. E. Lux, K. M. John and V. Bennett, Nature, 1990, 344,36–42.

165 S. E. Lux, W. T. Tse, J. C. Menninger, K. M. John, P. Harris, O.Shalev, R. R. Chilcote, S. L. Marchesi, P. C. Watkins, V. Bennett,S. Mcintosh, F. S. Collins, U. Francke, D. C. Ward and B.Forget, Nature, 1990, 345, 736–739.

166 P. Bork, Proteins: Struct., Funct., Genet., 1993, 17, 363–374.167 S. G. Sedgwick and S. J. Smerdon, Trends Biochem. Sci., 1999, 24,

311–316.168 P. Michaely, D. R. Tomchick, M. Machius and R. G. W.

Anderson, EMBO J., 2002, 21, 6387–6396.169 M. R. Groves and D. Barford, Curr. Opin. Struct. Biol., 1999, 9,

383–389.170 A. V. Kajava, J. Biol. Chem., 2002, 277, 49791–49798.171 E. R. G. Main, S. E. Jackson and L. Regan, Curr. Opin. Struct.

Biol., 2003, 13, 482–489.172 T. J. Boggon, J. Murray, S. Chappuis-Flament, E. Wong, B. M.

Gumbiner and L. Shapiro, Science, 2002, 296, 1308–1313.173 F. Cailliez and R. Lavery, Biophys. J., 2005, 89, 3895–3903.174 G. Lee, K. Abdi, Y. Jiang, P. Michaely, V. Bennett and P. E.

Marszalek, Nature, 2006.175 T. J. Richmond and C. A. Davey, Nature, 2003, 423, 145–150.176 K. Heichman and R. Johnson, Science, 1990, 249(4968),

511–517.177 B. Muller-Hill, The lac operon, Walter de Gruyter, New York,

1996.178 M. Lewis, G. Chang, N. C. Horton, M. A. Kercher, H. C. Pace,

M. A. Schumacher, R. G. Brennan and P. Lu, Science, 1996, 271,1247–1254.

179 A. M. Friedman, T. O. Fischmann and T. A. Steitz, Science, 1995,268, 1721–1727.

180 B. Tolhuis, R. Palstra, E. Splinter, F. Grosveld and W. de Laat,Mol. Cell, 2002, 10, 1453–1465.

181 M. Ptashne, A Genetic Switch, Cold Spring Harbor LaboratoryPress, Cold Spring Harbor, NY, 2004.

182 The Operon, ed. J. H. Miller and W. S. Reznikoff, Cold SpringHarbor Laboratory Press, Cold Spring Harbor, NY, 1980.

183 J. Vilar and L. Saiz, Curr. Opin. Genet. Dev., 2005, 15, 136–144.184 D. Swigon, B. D. Coleman and W. K. Olson, Proc. Natl. Acad.

Sci. U. S. A., 2006, 103, 9879–9884.185 A. Balaeff, L. Mahadevan and K. Schulten, Phys. Rev. E: Stat.

Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2006, 73, 031919.186 A. Balaeff, L. Mahadevan and K. Schulten, Phys. Rev. Lett.,

1999, 83(23), 4900–4903.187 A. Balaeff, C. R. Koudella, L. Mahadevan and K. Schulten,

Philos. Trans. R. Soc. London, Ser. A, 2004, 362, 1355–1371.188 A. Balaeff, L. Mahadevan and K. Schulten, Structure, 2004, 12,

123–132.189 C. E. Bell and M. Lewis, Nat. Struct. Biol., 2000, 7(3), 209–214.190 S. Oehler, E. R. Eismann, H. Kramer and B. Muller-Hill, EMBO

J., 1990, 9(4), 973–979.191 L. M. Edelman, R. Cheong and J. D. Kahn, Biophys. J., 2003, 84,

1131–1145.192 L. Finzi and J. Gelles, Science, 1995, 267, 378–380.193 L. Bintu, N. Buchler, H. G. Garcia, U. Gerland, T. Hwa, J.

Kondev, T. Kuhlman and R. Phillips, Curr. Opin. Genet. Dev.,2005, 15, 125–135.

194 J. W. Weisel, H. Shuman and R. I. Litvinov, Curr. Opin. Struct.Biol., 2003, 13(2), 227–235.

195 B. Marshall, M. Long, J. Piper, T. Yago, R. McEver and Z. C.,Nature, 2003, 423, 190–193.

196 J. M. Louis, I. J. Byeon, U. Baxa and A. M. Gronenborn, J. Mol.Biol., 2005, 348, 687–698.

197 M. Gao and K. Schulten, Structure, 2004, 12, 2096–2098.198 M. Jin, L. Andricioaei and T. A. Springer, Structure, 2004, 12(12),

2137–2147.199 E. Puklin-Faucher, M. Gao, K. Schulten and V. Vogel, J. Cell

Biol., 2006, submitted.200 W. Schubert, C. Urbanke, T. Ziehm, V. Beier, M. P. Machner, E.

Domann, J. Wehland, T. Chakraborty and d. W. Heinz, Cell,2002, 111, 825–836.

201 E. Conti, C. W. Muller and M. Stewart, Curr. Opin. Struct. Biol.,2006, 16(2), 237–244.

202 T. A. Isgro and K. Schulten, Structure, 2005, 13, 1869–1879.203 T. A. Isgro and K. Schulten, J. Mol. Biol., 2006, submitted.204 M. Weickert and S. Adhya, J. Biol. Chem., 1992, 267(22),

15869–15874.205 M. Geanacopoulos, G. Vasmatzis, V. Zhurkin and S. Adhya,

Nat. Struct. Biol., 2001, 8, 432–436.206 W. Humphrey, A. Dalke and K. Schulten, J. Mol. Graphics, 1996,

14, 33–38.

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